On complex Finsler spaces with Randers metric

Nicoleta Aldea; Gheorghe Munteanu

doi:10.4134/JKMS.2009.46.5.949

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2009; 46(5): 949-966

Printed September 1, 2009

https://doi.org/10.4134/JKMS.2009.46.5.949

On complex Finsler spaces with Randers metric

Nicoleta Aldea and Gheorghe Munteanu

Transilvania University

Abstract

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Abstract

In this paper we introduce in study a new class of complex Finsler spaces, namely the complex Randers spaces, for which the fundamental metric tensor and the Chern-Finsler connection are determined. A special approach is devoted to K\"{a}hler-Randers metrics. Using the length arc parametrization for the extremal curves of the Euler-Lagrange equations we obtain a complex nonlinear connections of Lorentz type in a complex Randers space.

Keywords: complex Finsler spaces, Randers spaces

MSC numbers: 53B40, 53C56